Multicomponent Polymer Systems - ACS Publications

10 Copolymerization in the Presence of

Downloaded by UNIV OF CALIFORNIA SAN DIEGO on January 18, 2016 | http://pubs.acs.org Publication Date: June 1, 1971 | doi: 10.1021/ba-1971-0099.ch010

Depolymerization Reactions PAUL WITTMER Kunststofflaboratorium der Badische Anilin- & Soda-Fabrik A G , Ludwigshafen am Rhein, Germany The copolymerization equation is valid if all propagation steps are irreversible. If reversibility occurs, a more com plex equation can be derived. If the equilibrium constants depend on the length of the monomer sequence (penulti mate effect), further changes must be introduced into the equations. Where the polymerization is subjected to an equilibrium, α-methylstyrene was chosen as monomer. The polymerization was carried out by radical initiation. With methyl methacrylate as comonomer the equilibrium con stants are found to be independent of the sequence length. Between 100° and 150°C the reversibilities of the homo polymerization step of methyl methacrylate and of the alternating steps are taken into account. With acrylonitrile as comonomer the dependence of equilibrium constants on the length of sequence must be considered.

T n general polymerizations proceed i n only one direction, so that we can write for a single step of the propagation reaction

A

Κ Pn* 4~ M —• Ρ · χ Λ

(1)

+

P'n is a reactive molecule of the polymer with η monomer units i n the chain, and it is unimportant whether the polymerization mechanism is radical or ionic. The rate constant of the propagation step is kp. Under certain conditions, monomer units can be split off the reactive polymer molecule. Then it is necessary to consider also the depolymerization reaction (with the rate constant k ). d

k

ρ · + M4P;+I Λ

140 In Multicomponent Polymer Systems; Platzer, Norbert A. J.; Advances in Chemistry; American Chemical Society: Washington, DC, 1971.

(2)

10.

WITTMER

141

Copolymerization and Depolymerization

According to Equation 2 each step of the propagation is an equihbrium for which Dainton and Ivin (2, 4) have found: Τ

=

± c

Δ

AS°

( = 0. In this case only the homopolymerization of the monomer M is reversible. W e can write the simpler equation (JO, 13,29): 2

x

x

In Multicomponent Polymer Systems; Platzer, Norbert A. J.; Advances in Chemistry; American Chemical Society: Washington, DC, 1971.

150

M U L T I C O M PONENT P O L Y M E R SYSTEMS

1 — Xi =

n g M J + J C Q + IMJ _ 1 / /rxgMJ + XQ + t M j y _ [Mi]

( 3 4 )

Special Case where K ^ 0, qi = 0, and 42 = 0. In this case the two homopolymerization reactions are reversible; the alternative steps are irreversible. Here Equation 35 is valid (10,29):


2

1

+

r

i

[MJ [M7]-

Κχ r

i

,

(

[M7]

(

1

"

X

l

)

(35)

d[M

2

[M

t

X i is given by Equation 34, 1/1 by Equation 36: ( 1

_

y i )

r ([MJ + K ) + [MJ _ 2 T^fii

=

l / / r ( [ M J + K,) + [ M J V ί \ 2 ΤΚ /

t

2

2

2

2

[MJ K

2

(36) Special Case where K = 0, q\ = 0, and q = 0. Equilibrium Con stant Ki Depends on the Chain Length. According to Szwarc and co workers (12, 26) the equilibrium constants of the anionic polymerization of α-methylstyrene depend on the degree of polymerization (chain lengths). For the reaction 2

CH3

2

CH3

CH3

CH3

I

^1

CH3

I

CH3

I I

θ C — C H — C H — C θ + C H = C and to calculate the copolymerization curves, a com puter was used. W i t h rising temperature q increases; q\ is zero, and it appears reasonable to assign a small positive value to q\ only at the high est temperature explored—i.e., 150°C. The results are shown in Figure 9. x

2


10.

Copolymerization and DepolymeHzation

wiTTMER

m o l - 7 . in polymer


ι

^ ι

30mol- /o in monomer e

—

501

50

•

— rc-

1 '

' — ' — — ι — -

150

100

M » 50mol -7o in monomer 1

m o l - 7 · in polymer A

50Ï

0

Mi-VOmol- /© in monomer m o l - 7 · in polymer

50f

siT —

,

H

~ 100 T*C—•

'

'

' 150

ΜΊ - 8 0 mol - 7© in monomer mol - 7· in polymer

Figure 11. Composition of copolymers as a function of the polymenzation temperature. Calculated by Equa tions 17 and 33. Dotted curves calcufoted by Equation 33.


165


166

M U L T I C O M P O N E N T P O L Y M E R SYSTEMS

The calculated curves agree well with the measured values. A t low concentrations of α-methylstyrene (lower left corner of the diagram) there are greater deviations. The experimentally measured concentra tions of α-methylstyrene he above the calculated ones. This difference cannot yet be explained. It is noteworthy that the statistical deviation is higher than at lower temperatures. The parameter q> is by definition a quotient of two rate constants. Therefore, its temperature dependence should follow the Arrhenius equa tion (Figure 10). The differences in activation energies are calculated to be AEq

= En — E

2

l2

= 25 kcal/mole

Figure 11 shows a compilation of the compositions of the polymers which have been polymerized from different monomer mixtures as a function of polymerization temperature. The curves plotted next to the measured points were calculated at temperatures below 100 °C by Equation 33 and at temperatures above 100 °C by Equation 17. The dotted curves for temperatures above 100 °C were calculated by Equation 33. In addi tion to the measured values taken from Tables III and V , Figure 11 also contains some measured points at 0 ° C . Polymerization was done i n flasks which were stored in a thermally controlled room for a long time ( e.g., with 30 mole % α-methylstyrene, 34 days, with 50 and 70 mole % , 166 days ). It is apparent that the curve derived by Equation 17 agrees well with the measured points. However, the dotted curve at higher temperatures, calculated b y Equation 33 shows significant deviations. Table VI.

Copolymerization of α-Methylstyrene ( M i ) and Acrylonitrile ( M o )

Mi mole % in Monomer Mixture

0°C

5 10 20 30 40

40.1! 45.8 48.8 50.6 51.6o

M

h

5

8

4

mole % in Polymer

20°C

50°C

39.09

6

36.5 42.3 47.5, 49.6

9

5Ο.63

44.4 48.2 50.5 51.9

0

0

2

9

5

60°C 35.67

42.7 46.7 49.8o 51.5 7

70°C 35.2

34.02

41.69

41.2 46.0 49.0 50.8a

e

53.6i

46.9 49.9 51.7i 51.5 53.7

54.6 57.1

8

54.87

6

57.12

9

X

80°C

6 e

7

52.89

52.4

7

52.3 53.3 54.7 56.4

e

3

32.8ο 39.63

53.12

45.4 48.5 50.7 50.8ο 52.8o

54.04 55.9

54.4 56.8

8

7

3

50 55.78 60 70 80 80.29 90 95

100°C

3

8

9

8

53.9 55.0 58.1

4

53.69

8

S6.O7

62.5 67.2

9

64.2

7

68.80

s

59.1

2 2

6

6

59.82

5

0

7

59.7, 65.3 6

60.1 65.5

2

2

60.15 65.2

4

58.9 64.1

2

e




wiTTMER

Figure 12. Copolymerization of α-methylstyrene and acrylonitrile. Curves calculated by Equation 5 for 0% 20% 50% 60% 70% 80% and 100°C.


168



Measurements on α-Methylstyrene—Acrylonitrile. Polymerizations were carried out in dilatometers without solvent. Initiator was azobisisobutyronitrile. A t 100 °C the reaction was initiated thermally. A t 0° and 20 °C the reaction was carried out in flasks in a thermally controlled room. Yields were below 5 % . The composition of the copolymers was calculated from nitrogen determination (Kjeldahl method). In an older reference (29) polymerizations were carried out at 20°, 50°, 60°, and

3,6

Figure 13.

Ό'

Dependence on temperature of r values used in Equation 5

70°C. The copolymerization parameters, derived from Equation 33 yielded a straight line in an Arrhenius plot. This led to the conclusion that the sequence of two monomer units is subject to the same polymerization-depolymerization equilibrium as in the case for longer sequences. This must be corrected if one considers a wider temperature range. Table V I shows the result of the measurements. Here too it is possible to use the Mayo equation to describe the measurements if the copoly merization parameters at each polymerization temperature are chosen properly (Figure 12). If the logarithm of the measured values is plotted against the reciprocal of absolute temperature, a small deviation from the straight line for ri is observed; this is shown in Figure 13. In the following the reversibility of the polymerization of α-methyl styrene has been considered. The copolymerization curves were calcu-


wiTTMER



10.

Figure 14. Copolymerization of a-meihylstyrene and acrylonitrile. Curves calculated by Equation 33 for 0°, 20°, 50% 60°, 70°, 80°, and 100°C.


169


170


lated by Equations 33 and 34. As Figure 14 shows a proper choice of the copolymerization parameters yields a good description of the measured points. Only at the highest polymerization temperature investigated (100°C) is there a deviation to higher values at the highest concentra tions of α-methylstyrene. Even in choosing higher numerical values for ti it is impossible to get better agreement in the upper part of the curve without losing good agreement in the lower part. Figure 15 shows that the copolymerization parameter η used i n Equation 33 does not follow the Arrhenius equation. In a previous pub lication (29) measurements were carried out only in the temperature

Figure 15.

Dependence on temperature of r values used in Equation 33

range 20°-70°C. In this range τ still follows the Arrhenius law. Meas urements in a wider temperature range, however, demonstrate that this is a purely formal agreement without any real meaning. Figure 16 shows data calculated by Equation 37. This calculation includes the condition that sequences of two monomer units do not depolymerize. Here too, good agreement is reached between the measured points and calculated curves. The r values in Figure 16 follow the Arrhenius equation as shown in Figure 17. The differences in activation energies are calculated to be λ

E

n

-

E

12

= 1.87 kcal/mole

Εη — Ε 2i = 1.46 kcal/mole



wiTTMER


Multicomponent Polymer Systems - ACS Publications

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